Math 300: Mathematical Computing

Matlab ICE

Create a Matlab function that does an adaptive trapezoidal rule.
The function should take four arguments: the function whose
integral is to be approximated; the left endpoint of the interval
of integration; the right endpoint; and a tolerance for changes
in the estimate of the integral. The last quantity is key. The function
will approximate the integral with a simple, single-interval
trapezoidal rule, and then again with a two-interval trapezoidal
rule. It will compare the two values, and if the absolute value
of the difference between them is smaller than the tolerance,
then it declares victory.

Note that this function will use recursion. Care will be required to avoid
mistakes of infinite recursion.